GIG: Infrastructure Improvement for a Research Group for the Study of the Algebra and Geometric of Quantum Physics

9510375 Yetter关注由量子物理引起或与之相关的数学问题已成为堪萨斯州立大学数学系进行的许多数学研究的压倒一切的主题。这个项目解决了从事这一领域数学研究的小组的基础设施需求，特别是使小组能够聘请一名博士后研究助理，他的存在将通过注入新的观点和想法以及加强小组成员之间的联系并改善小组可用的计算环境来提高研究效率。小组的研究兴趣范围从非常经典的数学应用到量子理论--解薛定谔方程(L.V.KAPITANSKI)，量子散射问题(正反问题)(A.G.Ramm和K.VANINSKY)，和连续统统计力学(K.Vaninsky)--从一般的量子化问题(Y.Soibelman)和非对易几何(F.Wu和G.Nagy)到与代数、拓扑和量子场论相关的最新发展-量子群(Z.Lin和Y.Soibelman)，拓扑场和共形场理论(L.Crane，Z.Lin和D.N.Yetter)，规范理论在微分拓扑学中的应用(F.Miller)，以及西格玛模型(L.V.Kapitanski)。(本项目每个共同PI的第一次提到都是大写的。)

9510375 Yetter A focus on mathematical problems arising from or related to quantum physics has become the over-riding theme of much of the mathematical research carried out in the Kansas State University Department of Mathematics. This project addresses the infrastructure needs of the group engaged in mathematical research in this area, specifically enabling the group to hire a postdoctoral research assistant whose presence will improve research productivity through the injection of fresh perspectives and ideas and the cementing ties between members of the group and providing for improvements to the computing environment available to the group.Research interests in the group range from very classical applications of mathematics to quantum theory--- solution of equations of Schroedinger type (L.V. KAPITANSKI), quantum scattering problems (both direct and inverse) (A.G. Ramm and K. VANINSKY), and continuum statistical mechanics (K. Vaninsky)---through general quantization problems (Y. SOIBELMAN) and non-commutative geometry (F. WU and G. Nagy) to recent developments relating algebra, topology and quantum field theory--- quantum groups (Z. LIN and Y. Soibelman), topological and conformal field theories (L. CRANE, Z. Lin, and D.N. YETTER), applications of gauge theory to differential topology (F. Miller), and sigma models (L.V. Kapitanski).(The first mention of each co-PI for the project is in upper-case.)